The Ezouidi Theorems: Beyond Abel A Complete Algebraic Framework for Polynomial Roots, Duality, and Hierarchies

This book presents a complete algebraic framework for solving polynomial equations of any degree. Based on the Seven Ezouidi Theorems, it establishes a triple duality between polynomials, linear equations, and matrices. Key innovations include a direct recurrence from power sums to elementary symmetric sums (bypassing Newton's identities), the EMST reduction with parity properties for arithmetic progressions, and full reverse duality from the nullspace of the Ezouidi matrix back to the original polynomial. All theorems are demonstrated for degrees 3 through 9 with three cases per degree: complex a/complex d, real a/complex d, and d = 0 (all roots equal). The framework works for any integer exponent q (positive, zero, or negative), generalizing the classical results of Viète, Newton, and Pascal.